5A. Vertical alignment

Question 1

What is the equation for the length (L) of a vertical crest curve when the sight distance is less than the length?

Answer 1

AASHTO Chapter 3: 3-42

L = (AS^2) / (100 (sqrt(2h1) + sqrt(2*h2))^2

where:

L = length of vertical curve, ft
A = algebraic difference in grades, percent
S = sight distance, ft
h1 = height of eye above roadway surface, ft
h2 = height of object above roadway surface, ft

Question 2

What is the equation for the length (L) of a vertical crest curve when the sight distance is more than the length?

Answer 2

AASHTO Chapter 3: 3-42

L = 2S - (200 *sqrt(h1) + sqrt(h2))^2 / (A)

where:

L = length of vertical curve, ft
A = algebraic difference in grades, percent
S = sight distance, ft
h1 = height of eye above roadway surface, ft
h2 = height of object above roadway surface, ft

Question 3

What is K?

Answer 3

Rate of vertical curvature
K = L / A

L = length
A = algebraic difference in grades

Question 4

Where can the design control for vertical crest curves based on stopping distance be found

Answer 4

AASHTO Green Book: Chapter 3: Table 3-35

Question 5

Where can the design control for vertical crest curves based on passing sight distance be found

Answer 5

AASHTO Green Book: Chapter 3: Table 3-36

Question 6

What are the steps to determine the height of a vertical curve at a specific station?

Answer 6

NCEES manual Chapter 5.3.1
Step one: Find PVC stationing and height.

Step two: Use parabolic curve formula
Curve Elevation = Ypvc + g1x +x^2((g2-g1)/(2L))
- L in stations
- grades as whole numbers

Step three: Find difference between PVC station and specific station
- This is x

Step four: Solve equation

Question 7

How can one find the slope of a vertical curve at a specific point?

Answer 7

NCEES manual Chapter 5.3.1

Take the derivative of the parabolic curve formula with respect to x.

Slope = g1 + x((g2-g1)/L)